Memoirs of the American Mathematical Society 1993; 107 pp; softcover Volume: 101 ISBN10: 0821825461 ISBN13: 9780821825464 List Price: US$29 Individual Members: US$17.40 Institutional Members: US$23.20 Order Code: MEMO/101/485
 Requiring only familiarity with the terminology of categories, this book will interest algebraic geometers and students studying schemes for the first time. Feit translates the geometric intuition of local structure into a purely categorical format, filling a gap at the foundations of algebraic geometry. The main result is that, given an initial category \({\mathcal C}\) of "local" objects and morphisms, there is a canonical enlargement of \({\mathcal C}\) to a category \({\mathcal C}^{gl}\) which contains all "global" objects whose local structure derives from \({\mathcal C}\) and which is functorially equivalent to the traditional notion of "global objects". Using this approach, Feit unifies definitions for numerous technical objects of algebraic geometry, including schemes, Tate's rigid analytic spaces, and algebraic spaces. Readership Graduate students studying schemes for the first time; algebraic geometers with interest in foundational issues. Table of Contents  Terminology
 Canopies
 Canopies and colimits
 Smoothing
 Local and global structures
